On Scattered Convex Geometries

Kira Adaricheva, Maurice Pouzet

Research output: Contribution to journalArticle

Abstract

A convex geometry is a closure space satisfying the anti-exchange axiom. For several types of algebraic convex geometries we describe when the collection of closed sets is order scattered, in terms of obstructions to the semilattice of compact elements. In particular, a semilattice Ω(η), that does not appear among minimal obstructions to order-scattered algebraic modular lattices, plays a prominent role in convex geometries case. The connection to topological scatteredness is established in convex geometries of relatively convex sets.

Original languageEnglish
Pages (from-to)1-28
Number of pages28
JournalOrder
DOIs
Publication statusAccepted/In press - Nov 21 2016

Keywords

  • Algebraic lattice
  • Convex geometry
  • Lattices of relatively convex sets
  • Lattices of suborders
  • Lattices of subsemilattices
  • Multi-chains
  • Order-scattered poset
  • Topologically scattered lattice

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology
  • Computational Theory and Mathematics

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  • Cite this

    Adaricheva, K., & Pouzet, M. (Accepted/In press). On Scattered Convex Geometries. Order, 1-28. https://doi.org/10.1007/s11083-016-9413-0